Competition of Dzyaloshinskii-Moriya and Higher-Order Exchange Interactions in $\mathrm{Rh}/\mathrm{Fe}$ Atomic Bilayers on Ir(111)

Using spin-polarized scanning tunneling microscopy and density functional theory we demonstrate the occurrence of a novel type of noncollinear spin structure in $\mathrm{Rh}/\mathrm{Fe}$ atomic bilayers on Ir(111). We find that higher-order exchange interactions depend sensitively on the stacking sequence. For fcc-$\mathrm{Rh}/\mathrm{Fe}/\mathrm{Ir}(111)$, frustrated exchange interactions are dominant and lead to the formation of a spin spiral ground state with a period of about 1.5 nm. For hcp-$\mathrm{Rh}/\mathrm{Fe}/\mathrm{Ir}(111)$, higher-order exchange interactions favor an up-up-down-down ($\uparrow \uparrow \downarrow \downarrow$) state. However, the Dzyaloshinskii-Moriya interaction at the $\mathrm{Fe}/\mathrm{Ir}$ interface leads to a small angle of about 4° between adjacent magnetic moments resulting in a canted $\uparrow \uparrow \downarrow \downarrow$ ground state.

Figure 1

(a) Perspective STM constant-current image of a typical $\mathrm{Rh}/\mathrm{Fe}/\mathrm{Ir}(111)$ sample with approximately 0.8 ML Fe and 0.4 ML Rh, colorized with the simultaneously acquired $dI/dU$ signal ($U=+0.5\mathrm{V}$, $I=0.75\mathrm{nA}$, $T=8\mathrm{K}$). (b) Calculated energy dispersions $E(\mathbf{q})$ of right-rotating cycloidal homogeneous spin spirals for fcc-Rh (left) and hcp-Rh (right) on $\mathrm{Fe}/\mathrm{Ir}(111)$ without spin-orbit coupling (black symbols) and with spin-orbit coupling (red symbols). The lines denote fits to the Heisenberg model including the Dzyaloshinskii-Moriya interaction for the case with spin-orbit coupling (see Ref. [33] for details). The energies of the $\uparrow \uparrow \downarrow \downarrow$ states along the two high symmetry directions are marked by blue crosses, and the spin structures are sketched as insets. Local geometry of the Fe atoms (red) in fcc and hcp stacking shown as insets.

Figure 2

(a),(c) SP-STM constant-current images of a fcc-Rh and a hcp-Rh island on $\mathrm{Fe}/\mathrm{Ir}(111)$, respectively, measured with a magnetic Cr tip, sensitive to the out-of-plane magnetization component of the sample (contrast level adjusted locally on the $\mathrm{Rh}/\mathrm{Fe}$ to $\pm 20\mathrm{pm}$; $T=8\mathrm{K}$, $U=+30$ and $-30\mathrm{mV}$, $I=1.0$ and 1.5 nA, respectively). (b),(d) Line profiles along the rectangles in (a) and (c); solid lines are fits with cosine functions. (e) Constant-current STM image of a Rh island with fcc and hcp stacking on fcc-$\mathrm{Fe}/\mathrm{Ir}(111)$ measured with a non-spin-polarized tip (contrast $\pm 15\mathrm{pm}$; $T=8\mathrm{K}$, $U=+15\mathrm{mV}$, $I=6\mathrm{nA}$). (f) Top-view sketches of a homogeneous 4 atom period spin spiral and of the $\uparrow \uparrow \downarrow \downarrow$ state; the bottom layer shows the Fe atoms and color and symbols indicate their magnetization directions; the top layer shows the Rh atoms and their size indicates the magnitude of their induced moments. The magnetic unit cells are indicated by the dotted boxes.

Figure 3

STM images calculated based on DFT for hcp-$\mathrm{Rh}/\mathrm{Fe}/\mathrm{Ir}(111)$ in the $\uparrow \uparrow \downarrow \downarrow$ state along $\overline{\mathrm{\Gamma }M}$. (a) STM image at a distance of $z=6.7\AA$ for a non-spin-polarized tip. (b) SP-STM image for a tip spin polarization of 0.5. Red and blue circles denote Fe atoms. Gray circles indicate Rh atoms and their size the magnitude of magnetic moments. Dots and crosses denote upward and downward moments. (c) Line scans along the $[11\overline{2}]$ direction for the images in (a) (green line) and in (b) (orange line). The integrated LDOS (ILDOS) has been calculated between the Fermi energy $E_F$ and $E_F-0.1\mathrm{eV}$.

Figure 4

(a),(b) Constant-current SP-STM images of a hcp-Rh island on $\mathrm{Fe}/\mathrm{Ir}(111)$ measured with out-of-plane sensitive and in-plane sensitive magnetic Fe-coated W tip, respectively; the tip magnetization ${\mathbf{m}}_{\mathrm{tip}}$ aligns in the applied out-of-plane field of $B=-2\mathrm{T}$ (a), but is in the sample surface plane without applied field (b); its direction as indicated is derived from comparison of the relative magnetic contrast amplitudes of the three symmetry-equivalent rotational domains, see enlarged images (all contrast levels adjusted locally to $\pm 15\mathrm{pm}$) ($T=8\mathrm{K}$, $U=+30\mathrm{mV}$, $I=3\mathrm{nA}$).

Figure 5

(a) Sketch of the canted $\uparrow \uparrow \downarrow \downarrow$ state defined by the angle $\alpha$. Only the magnetic moments in the Fe layer are shown. Blue and red denote an upward or downward out-of-plane magnetization component. (b) Energy as a function of $\alpha$ resolved by the contributions from different magnetic interactions. The filled circles are obtained numerically using the DFT interaction parameters for the atomistic spin model and the lines are from the analytical forms of the contributions (see text). Note that a positive (negative) value of $\alpha$ indicates a clockwise (anticlockwise) rotation of the magnetic moments.